The first wish list you create on Amazon is, by default, public -- anyone can see it, whether they know you or not, and it will appear in search results. Using Amazon's list management tool, you can change it, and any other wish list you create, to either shared or private. A shared wish list is not searchable, but you can give the address to others so they can see it; a private wish list, on the other hand, is truly private and visible only to you.
Open your wish list and click Manage Your Lists.
Select either Shared or Private from the drop-down menu by the name of the list, depending on your preference.
Click Submit to save your changes.
You can see whether each of your wish lists is public, shared or private in the list summary, located above the "Manage Your Lists" link.
When creating additional wish lists, you can choose whether they're public, shared or private immediately -- it's only the first wish list that is set to public by default.